{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:51:18Z","timestamp":1787028678966,"version":"build-2736575974"},"reference-count":16,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T00:00:00Z","timestamp":1754956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"German BMBF","award":["16SV8671"],"award-info":[{"award-number":["16SV8671"]}]},{"name":"German BMBF","award":["P2021-02-014"],"award-info":[{"award-number":["P2021-02-014"]}]},{"name":"Primflow Project, Andreas Hildebrandt the support of the Carl-Zeiss project TOPML","award":["16SV8671"],"award-info":[{"award-number":["16SV8671"]}]},{"name":"Primflow Project, Andreas Hildebrandt the support of the Carl-Zeiss project TOPML","award":["P2021-02-014"],"award-info":[{"award-number":["P2021-02-014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JCP"],"abstract":"<jats:p>Differential privacy (DP) is an important framework to provide strong theoretical guarantees on the privacy and utility of released data. Since its introduction in 2006, DP has been applied to various data types and domains. More recently, the introduction of metric differential privacy has improved the applicability and interpretability of DP in cases where the data resides in more general metric spaces. In metric DP, indistinguishability of data points is modulated by their distance. In this work, we demonstrate how to extend metric differential privacy to datasets representing three-dimensional rotations in SO(3) through two mechanisms: a Laplace mechanism on SO(3), and a novel privacy mechanism based on the Bingham distribution. In contrast to other applications of metric DP to directional data, we demonstrate how to handle the antipodal symmetry inherent in SO(3) while transferring privacy from S3 to SO(3). We show that the Laplace mechanism fulfills \u03f5\u03d5-privacy, where \u03d5 is the geodesic metric on SO(3), and that the Bingham mechanism fulfills \u03f5\u02dc\u03d5-privacy with \u03f5\u02dc=\u03c04\u03f5. Through a simulation study, we compare the distribution of samples from both mechanisms and argue about their respective privacy\u2013utility tradeoffs.<\/jats:p>","DOI":"10.3390\/jcp5030057","type":"journal-article","created":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T07:53:44Z","timestamp":1754985224000},"page":"57","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Metric Differential Privacy on the Special Orthogonal Group SO(3)"],"prefix":"10.3390","volume":"5","author":[{"given":"Anna Katharina","family":"Hildebrandt","sequence":"first","affiliation":[{"name":"PRAIVACY UG, Science Park 1, 66123 Saarbr\u00fccken, Germany"},{"name":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5652-2591","authenticated-orcid":false,"given":"Elmar","family":"Sch\u00f6mer","sequence":"additional","affiliation":[{"name":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2180-6516","authenticated-orcid":false,"given":"Andreas","family":"Hildebrandt","sequence":"additional","affiliation":[{"name":"Mondata GmbH, Science Park 1, 66123 Saarbr\u00fccken, Germany"},{"name":"Institute for Computer Science, Johannes Gutenberg University Mainz, 55122 Mainz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1561\/0400000042","article-title":"The algorithmic foundations of differential privacy","volume":"9","author":"Dwork","year":"2014","journal-title":"Found. Trends Theor. Comput. Sci."},{"key":"ref_2","unstructured":"Fernandes, N. (2021). Differential Privacy for Metric Spaces: Information-Theoretic Models for Privacy and Utility with New Applications to Metric Domains. [Ph.D. Thesis, \u00c9cole Polytechnique de Paris, Paris, France, and Macquarie University]."},{"key":"ref_3","unstructured":"Fan, L. (2018, January 16\u201318). Image pixelization with differential privacy. Proceedings of the Data and Applications Security and Privacy XXXII: 32nd Annual IFIP WG 11.3 Conference, DBSec 2018, Bergamo, Italy. Proceedings 32."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"101951","DOI":"10.1016\/j.cose.2020.101951","article-title":"Privacy preserving face recognition utilizing differential privacy","volume":"97","author":"Chamikara","year":"2020","journal-title":"Comput. Secur."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Weggenmann, B., and Kerschbaum, F. (2018, January 8\u201312). 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